Skip to main content

Methodological approaches for delimitating mixing zones in rivers: establishing admissibility criteria and flow regime representation


The present paper addresses defining the extent of the mixing zones of effluents discharged into rivers, which is a problem that should be analyzed based on probabilistic terms, as it is governed by several random processes. A river’s flow regime is one of the main variables, and it has a high dependence on hydrological processes. Additionally, after calculating the extent of the mixing zone, it is necessary to determine if the resulting dimensions are admissible or not. Common practice includes the admissibility criteria associated with the geometry of the river. However, this practice does not consider the environmental characteristics of the river that make it capable of absorbing the impact of the effluent (the biological and hydromorphological status of the river and the presence of structures that can change the river flow conditions, ecologically sensitive area or threatened species). This paper presents work on two important topics: on the one hand, the development of a methodology to establish the admissible extent of the mixing zone as a function of the environmental vulnerability of the river to the discharged effluent and, on the other hand, the proposal of a procedure to perform the calculations of the effluent mixing considering the variability of the river’s flow regime. The proposed methodological approaches are illustrated with an application to a real case, including a numerical simulation of the hydrodynamic and effluent evolution of the river during a year, to test the proposed methodology’s suitability and demonstrate the important savings in computational effort that can be achieved.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25


  1. ANZECC, ARMCANZ (2000) Australian and New Zealand guidelines for fresh and marine water quality: volume 2—aquatic ecosystems—rationale and background information. Technical report, Australian and New Zealand Environmental and Conservation Council

  2. Alvarez C, Juanes J, Revilla J, García A (2006) A two dimensional hydrodynamic model for the study of instream flows in rivers. In: 7th international conference on hydroinformatics. HIC 2006, Nice, France

  3. Bárcena J (2015) Desarrollo de una metodología para delimitar zonas de mezcla de vertidos industriales en estuarios. Tesis doctoral, Universidad de Cantabria

  4. Bárcena JF, García-Alba J, García A, Álvarez C (2016) Analysis of stratification patterns in river-influenced mesotidal and macrotidal estuaries using 3D hydrodynamic modelling and K-means clustering. Estuar Coast Shelf Sci 181:1–13

    Article  Google Scholar 

  5. Bárcena JF, Gómez AG, García A, Juanes JA (2017) Quantifying and mapping the vulnerability of estuaries to point-source pollution using a multi-metric assessment: the Estuarine Vulnerability Index (EVI). Ecol Ind 76:159–169

    Article  Google Scholar 

  6. Biron P, Ramamurthy A, Han S (2004) Three-dimensional numerical modeling of mixing at river confluences. J Hydraul Eng 130(3):243–253

    Article  Google Scholar 

  7. Camacho-Muñoz D, Martín J, Santos J, Aparicio I, Alonso E (2014) Occurrence of surfactants in wastewater: hourly and seasonal variations in urban and industrial wastewaters from Seville (Southern Spain). Sci Total Environ 468:977–984

    Article  Google Scholar 

  8. Cailleaud K, Michalec F, Forget-Leray J, Budzinski H, Hwang J, Schmitt F, Souissi S (2011) Changes in the swimming behavior of Eurytemora affinis (Copepoda, Calanoida) in response to a sub-lethal exposure to nonylphenols. Aquat Toxicol 102(3–4):228–231

    Article  Google Scholar 

  9. CCME (1999) Canadian environmental quality guidelines

  10. CCME (2003) Guidance on the site-specific application of water quality guidelines in Canada: procedures for deriving numerical water quality objectives. Technical report, Canadian Council of Ministers of the Environment

  11. Chin D (1985) Outfall dilution: the role of a far-field model. J Environ Eng 111(4):473–486

    Article  Google Scholar 

  12. David A, Tournoud M, Perrin J, Rosain D, Rodier C, Salles C, Bancon-Montigny C, Picot B (2012) Spatial and temporal trends in water quality in a Mediterranean temporary river impacted by sewage effluents. Environ Monit Assess 185(3):2517–2534

    Article  Google Scholar 

  13. del Barrio P, García A, García J, Alvárez C, Revilla JA (2012) A model for describing the eutrophication in a heavily regulated coastal lagoon. Application to the Albufera of Valencia (Spain). J Environ Manag 112:340–352

    Article  Google Scholar 

  14. Doneker R, Jirka G (2002) Boundary schematization in regulatory mixing zone analysis. J Water Resour Plan Manag 128:46–56

    Article  Google Scholar 

  15. EC (2010a) Technical guidelines for the identification of mixing zones pursuant to art. 4(4) of the directive 2008/105/EC. Technical report, European Commission

  16. EC (2010b) Technical background document on identification of mixing zones. Technical report, European Commission

  17. Einav R, Harussi K, Perry D (2002) The footprint of the desalination processes on the environment. Desalination 152(1–3):141–154

    Google Scholar 

  18. García A, Sainz A, Revilla JA, Álvarez C, Juanes JA, Puente A (2008) Surface water resources assessment in scarcely gauged basins in the north of Spain. J Hydrol 356(3–4):312–326

    Article  Google Scholar 

  19. García A, Juanes JA, Álvarez C, Revilla JA, Medina R (2010) Assessment of the response of a shallow macrotidal estuary to changes in hydrological and wastewater inputs through numerical modeling. Ecol Model 221:1194–1208

    Article  Google Scholar 

  20. Guevara A (1996) Control de calidad del agua. Análisis de las normas de control de la calidad de las aguas. Centro Panamericano de Ingeniería Sanitaria y Ciencias del Ambiente. OMS, Lima

    Google Scholar 

  21. Hall T, Fisher R, Rodgers J, Minshall G, Landis W, Kovacs T, Firth B, Dube M, Deardoff T, Borton D (2008) A long-term, multitrophic level study to assess pulp and paper mill effluent effects on aquatic communities in four US receiving waters: background and status. Integr Environ Assess Manag 5(2):189–198

    Article  Google Scholar 

  22. Kruk A (2004) Decline in migratory fish in the Warta River, Poland. Ecohydrol Hydrobiol 4(2):147–155

    Google Scholar 

  23. Kumar A, Tewary B, Banerjee M, Ahmad M (2010) A simplified approach for removal of suspended coal fines from black water discharge of mining and its allied industries. J Mines Met Fuels 58(11–12):346–348

    Google Scholar 

  24. Laraque A, Loup G, Filizola M (2009) Mixing processes in the Amazon River at the confluences of the Negro and Solimões Rivers, Encontro das Águas, Manaus, Brazil. Hydrol Process 23(22):3131–3140

    Article  Google Scholar 

  25. Lung W (1995) Mixing-zone modeling for toxic waste-load allocations. J Environ Eng 121(11):839–842

    Article  Google Scholar 

  26. Morán-Tejeda E, López-Moreno J, Ceballos-Barbancho A, Vicente-Serrano S (2011) River regimes and recent hydrological changes in the Duero basin (Spain). J Hydrol 3–4(11):241–258

    Article  Google Scholar 

  27. Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I—a discussion of principles. J Hydrol 10(3):282–290

    Article  Google Scholar 

  28. Pérez E (2010) Methodological approach for the establishment of the mixing zone of the discharge of the wastewater treatment plant of Casar de Periedo in the Saja River. Environmental Management of Hydraulic Systems, Universidad de Cantabria, Santader

    Google Scholar 

  29. Roberts P, Sternau R (1997) Mixing zone analysis for coastal wastewater discharge. J Environ Eng 123(12):1244–1250

    Article  Google Scholar 

  30. Rodríguez A, García A, Álvarez C (2016) Definition of mixing zones in rivers. Environ Fluids Mech 16(1):209–244

    Article  Google Scholar 

  31. Rodríguez A (2016) Metodología para el análisis de zonas de mezcla de vertidos puntuales en medios fluviales. Tesis doctoral, Universidad de Cantabria

  32. Salomons W (1995) Environmental impact of metals derived from mining activities: processes, predictions, prevention. Environ J Geochem Explor 25(1):5–23

    Article  Google Scholar 

  33. Sinton L, Hall C, Lynch P, Davies-Colley J (2001) Sunlight inactivation of fecal indicator bacteria and bacteriophages from waste stabilization pond effluent in fresh and saline waters. Appl Environ Microbiol 68(3):1122–1131

    Article  Google Scholar 

  34. USEPA (1991) Technical support document for water quality-based toxic control. Technical report, U.S. Environmental Protection Agency

  35. USEPA (1992) Technical guidance manual for performing waste load allocations, book III: estuaries. Technical report, U.S. Environmental Protection Agency

  36. USEPA (1994) Water quality standards handbook, 2nd edn. Technical report, U.S. Environmental Protection Agency

  37. USEPA (1995) Allocated impact zones for areas of non-compliance. Technical report, U.S. Environmental Protection Agency

  38. USEPA (1996) Npdes permit writer’s manual. Technical report, U.S. Environmental Protection Agency

  39. USEPA (2010) Npdes permit writer’s manual. Technical report, U.S. Environmental Protection Agency

  40. Xu J, Lee J, Yin K, Liu H, Harrison P (2011) Environmental response to sewage treatment strategies: Hong Kong’s experience in long term water quality monitoring. Mar Pollut Bull 62(11):2275–2287

    Article  Google Scholar 

Download references


The authors wish to give special thanks to Javier F. Bárcena of IH Cantabria for his valuable cooperation in the development of the present research.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Alonso J. Rodríguez Benítez.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rodríguez Benítez, A.J., Álvarez Díaz, C., García Gómez, A. et al. Methodological approaches for delimitating mixing zones in rivers: establishing admissibility criteria and flow regime representation. Environ Fluid Mech 18, 1227–1256 (2018).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: